IOP PUBLISHING SMART MATERIALS AND STRUCTURES

Smart Mater. Struct. 21 (2012) 065013 (8pp) doi:10.1088/0964-1726/21/6/065013

A bidirectional shape memory alloyfolding actuator

Jamie K Paik1 and Robert J Wood2

1 School of Engineering, Ecole Polytechnique Federale de Lausanne, Switzerland2 School of Engineering and Applied Sciences, Harvard University, USA

E-mail: jamie.paik@epfl.ch

Received 1 November 2011, in final form 19 March 2012Published 22 May 2012Online at stacks.iop.org/SMS/21/065013

AbstractThis paper presents a low-profile bidirectional folding actuator based on annealed shapememory alloy sheets applicable for meso- and microscale systems. Despite the advantages ofshape memory alloys—high strain, silent operation, and mechanical simplicity—theirapplication is often limited to unidirectional operation. We present a bidirectional foldingactuator that produces two opposing 180◦ motions. A laser-patterned nickel alloy (Inconel600) heater localizes actuation to the folding sections. The actuator has a thin (<1 mm)profile, making it appropriate for use in robotic origami. Various design parameters andfabrication variants are described and experimentally explored in the actuator prototype.

(Some figures may appear in colour only in the online journal)

1. Introduction

Shape memory alloys (SMAs) are attractive engineeringmaterials due to their ability to memorize shapes througha thermally induced solid state phase transition [1,2]. The material composition (e.g. Cu–Zn, Cu–Zn–Al,Cu–Al–Ni, Ni–Ti, Ni–Ti–Fe, Fe–Pt) largely determines themechanical properties including ductility, corrosion, and‘memory’ properties of the alloy. There are three categoriesof SMA shape changing effects that are derived fromcrystal reorientation during a reversible high-temperatureaustenite and low-temperature martensite phase change: thepseudoelastic effect, the one-way effect, and the two-wayeffect [3, 2]. The pseudoelastic effect exhibits no visibleplastic deformation by temperature or through loading. Theone-way effect is characterized by shape change upon loading,but no reorientation upon cooling. Once deformed, the‘memorized’ shape is recovered when heated above thetransition temperature. The two-way effect refers to shapechange upon cooling and heating without external loading.

The one-way effect is the basis of most SMA actuatorsand often requires antagonistic springs or actuators to induceloading. The addition of antagonistic actuators is not anattractive solution for producing repeated motions becauseof added complexity. When applying a ‘reverse’ load, apreloaded spring or superelastic-NiTi element are popular

methods to de-twin SMA actuators [4, 5]. However, to theauthors’ knowledge there is no example of a one-way SMAactuator that produces two motions in a single device. Thetwo-way effect is desirable as an actuator property becauseit allows repeated shape changes with temperature controlwithout an antagonist. However, upon variable loading,the two-way effect is minimized, and its strain is not aspronounced as in the one-way effect.

Therefore, for the application of robotic origami [1, 6]that requires multiple sequential foldings of tiled sheets, weseek low-profile actuators which use a single actuator inrecovering the original shape.

In this paper, we present the design and fabrication ofa compact SMA bidirectional actuator that produces twoopposing rotational motions with a high torque density anda low profile. The actuator’s two rotational axes are nearlyco-linear and each capable of up to 180◦ of rotation. TheSMA bidirectional actuator is activated by a thin externalheater that allows focused heating designed specifically forthis application.

2. Related work

The choice of actuator for modular robots in general,and robotic origami in particular, is a critical aspect ofdesign. For robotic origami [1, 6], the actuator must

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Smart Mater. Struct. 21 (2012) 065013 J K Paik and R J Wood

conform to submillimeter geometry of a tiled sheet whileproducing enough torque to create a sequence of foldings.SMA actuators are common in applications that have strictgeometric restrictions. Son introduced a linearity enhancedSMA wire actuator with reverse hysteresis control tominimize the shape variation [7]. Similarly, Constanza’snitinol one-way shape memory springs are controlled usinga detailed thermomechanical characterization and actuatordesign [8]. A previously reported low-profile torsionalactuator produces a high torque but only in a singledirection [1]. In another example, a wearable supportivedevice enhances facial expressiveness with an SMA wireactuator [9]. Some millimeter-scale linear micro-actuatorsuse bent ribbons of thin SMA and produce 420–570 µmdeflection depending on the antagonistic spring design [10].While this deflection is impressive considering the scale, thereare challenges with scaling up as it will be difficult to usewithout the silicon wafer backing. These examples of SMAactuators are suitable for their specific millimeter-scale tasksbut not applicable for robotic origami without significantlyaltering the current tiled sheet design.

In order to produce multiple shapes from the sameorigami, the sheet must be flat before being activated intoa new shape. This requires each folding edge to fold intwo directions (in and out). We can consider embedding twosingle direction actuators at a cost of additional mechanismsand weight. Some SMA actuators can produce two shapesby using mechanical compliance to move between minimumenergy shapes upon activation. Kohl presented a millimeter-scale gas microvalve made with a sputter-coated SMAthin film. Its photo-etched shape and different compositionallows an increased transition temperature [11]. However,the thin film application of SMA is yet to be applicablefor deflections larger than 1 mm. Tung’s laser-machineddesign of SMA tubing makes a catheter structure compliantin desired directions (with a high deflection) with sensorsmade of superelastic SMA [12]. However, it only producesmotion in one direction. Actuators that use the two-wayeffect typically have bistable shapes and often require noantagonistic structure. Mineta designed a 8 µm two-wayactuator by sputter coating TiNiCu and flat annealing thestructure [13]. Their actuator is made of SMA thin film thatis appropriate for nanoscale gripping. This design is difficultto scale up since the strain increases proportionally to thesize and the thickness of the structure. Kim et al presented atwo-way shape memory effect in their millimeter-scale SMAthat is usually unstable under loading. They showed that byinducing compressive loading cycles, it is possible to createmore robust two phase shapes by ‘training’ the material [14].This process may be applicable for thicker and larger scaleactuators but for low-profile actuators, the effect of the cyclicloading process is uncertain and requires extensive materialtreatment. For thinner materials this could cause additionalfatigue and even early stress fractures.

An actuator with a high torque density and a low profileis more achievable in using thin films, springs, and ribbonsof SMAs. However, it is extremely rare to find a structureor actuator that enables robust, active bidirectional actuation

without having antagonistic structure or manual loading.Ancillary loading mechanisms often add to the overall volumeof the actuation system and net power consumption as theactive actuator must overcome the ‘reverse’ loaded systemto produce desired work. Our design maintains a low profileand enables bidirectional motions in a single 500 µm thickactuator.

3. Bidirectional actuator design and fabrication

The complexity in designing a multi-directional SMA actuatoris in creating distinct motions using a single material.The most versatile actuator would produce multi-directionalactuation along collinear axes, or axes which intersect ata single point, a trait which is especially valuable forsmall-scale applications. The presented bidirectional actuatordesign minimizes the separation of two actuating axes withoutinterfering with the resulting torque and range of motion. Theengineering challenge lies in creating distinct activation areaswhich can be annealed, fabricated, and actuated.

3.1. Design choices

The majority of SMA actuators use Joule heating to excitethe phase transition. This is a common method to actuateSMA actuators because of its design and control simplicity.However, due to the inherently low resistivity of metal-basedSMA materials, substantial current is typically required. Thishigh current can cause problems for associated electricaltraces due to I2R losses. Previously, the authors proposedan alternative heating method for SMA actuators thatuses an external heater made of coiled Ni–Cr to generateheat [1]. This method showed superior power efficiencyand response times compared to Joule heating due to itsability to focus the heating area while requiring significantlylower currents. Pertaining to the actuator performance,the heating method is irrelevant provided that sufficientheating is supplied. However, a localized activation methodis required for a bidirectional actuator or any thermallyactivated multi-directional SMA actuator because they requireconcentrated heating in selected regions of movement. Withconventional Joule heating, producing selective heating isdifficult as discrete current paths are difficult to achieve.

Our designs for low-profile actuators rely on thin NiTisheets and an annealing process as described below. TheSMA material thickness is directly proportional to thetorque output (i.e. the folded and annealed cross-sectionalarea is proportional to the produced torque). Althoughhigh torque-to-volume is almost always desirable in rotaryactuators, the thickness of the SMA sheet material is limitedby the maximum strain of the material. Figure 1 shows the2D outline of the actuator and its dimensions along with theheater. We use 0.1 mm thick sheets which are compatiblewith our machining and annealing techniques. This thicknessis also appropriate for conductive heating from the externalheater that can initiate the thermally activated actuator withinseconds.

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Smart Mater. Struct. 21 (2012) 065013 J K Paik and R J Wood

Figure 1. Schematics of the bidirectional SMA actuator.Laser-machined outline of the actuator (a), heater and actuatordimensions (b).

3.2. Fabrication process

The actuator is composed of an SMA folding substrate anda heating element. The SMA sheet is laser machined whileflat, then folded and annealed to create new memorized shapesin different regions. As a result of the combination of 2Dmachining and folding, the designer can create a large range ofmotions as reported in [1]. We also propose unique solutionsto thermal activation with a heating element and attachment tothe NiTi SMA, which is notorious for its poor solderability.

3.2.1. Actuator. Our design focuses on creating twoopposing torques in a single actuator while keeping theaxes of rotation close so that two torques would be nearlycollinear. We used NiTi sheets with a transition temperatureof 65 ◦C (0.1 mm M alloy from Memry-Metale GmbH (www.memry.com)). To . form a desired 3D shape, we followedthe annealing process established in [1]. In the case ofa single actuator producing a 180◦ folding motion, dowelpins prescribed the radius of curvature. However, for thebidirectional actuator, we incorporated features into the designto produce a consistent radius of curvature without toolingby introducing sacrificial tabs and slots. Figure 1 illustratesa laser-machined SMA sheet with two actuating regions andtheir rotation of axes. The radius of curvature was governedby the length of the material between the slot and the tab.

Figure 2. Schematics of the bidirectional SMA actuatorfabrication. Laser-machined actuator outline from SMA sheet (a),opposingly interlaced tabs for creating uniform curvature forbidirectional actuating regions: here the tabs are used to anchor theshape (b), once removed from the jig the tabs are trimmed (c), eachactuating region is unfolded (d), and the actuator is mounted alongthe folding axis between tiles of a robotic origami structure (e).

We chose this to be 3 mm making the radius of curvatureto be less than a quarter of a millimeter. This relationship ischaracterized by the length of the active region which forms acircle made when rolled up. Therefore, having the slot in thecenter allowed two ends of the tab to interlace to form a tightand consistent curvature during and after annealing (figure 2).We used a jig to anchor the two ends and maintain the shape.The jig was designed with a socket-head cap screw spaced byspherical washers on each end that controls a lever arm withmultiple sets of pegs (figure 3). We applied constant pressureon the actuator by adjusting the force of the lever arm. Theentire jig is placed in a furnace preheated to 400 ◦C for30 min and then removed and quenched to room temperaturein running tap water. Once removed from the jig, the tabs wereremoved from the slot by unfolding the actuating axes. Thelong tabs were trimmed off close to the bolt holes.

3.2.2. Flex-heater. Having a heating element thatconcentrates heating at a specific area is critical for thebidirectional SMA actuator. We have experimented withtwo ways of fabricating the heater. One was by directlyattaching or ‘printing’ the heater on the actuator body

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Smart Mater. Struct. 21 (2012) 065013 J K Paik and R J Wood

Figure 3. Annealing jig for maintaining shape during annealing. The inset shows the actuator when the tabs are interlaced and placed onthe jig.

Figure 4. ‘Printed-on’ heater on the surface of the SMA actuator.

in the pre-annealed state and another was by attachinga heater after fabrication. For the ‘printed-on’ heater, wesandwiched the heating path between layers of insulators.We spin-coated (Specialty Coating Systems, Spincoat G3P-8)the laser-machined SMA with an adhesion promoter (T9039HD MicroSystems). Once vapor-cured under nitrogen gas(Rapid Thermal Processor, RTP-600xp), it was again spin-coated with polyimide precursor HD 4110 which has amaximum operating strain of 40%. Polyimide precursors arespin-coatable and can achieve a uniform thickness (about

2–3 µm) on the substrate surface. The insulated SMA wasthen oxygen plasma treated before being placed in a vacuumchamber for sputter coating. We sputter-coated Cr and Cu(0.01 and 0.1 µm respectively) and dry-etched the heaterpatterns using a DPSS laser. A second polyimide layer wasused for insulation (figure 4).

However, this ‘printed-on’ heater delaminated whenunder high strains associated with the current annealingmethod (approximately 10% strain, limited by the fracturestrain of the NiTi sheet). This solution was applicablefor lower strain cases when using thinner substrates or alarger radius of curvature. For the given dimensions of thecurrent bidirectional actuator (that produces approximately20% strain), we designed an external heater made ofpolyimide-Inconel 600 (72% Ni, 14–17% Cr, and 6–10%Fe). With a polyimide layer as a backing (35 µm polyimideand 40 µm Inconel 600), we followed a similar process toflex-circuit fabrication to make a flexible heating layer. Wefirst coated the Inconel 600 sheet in photoresist (Shipley 24Dpositive photoresist). The negative heater path design wasdirectly exposed to a DPSS UV laser and etched with FeCl3.The heater outline was then cut out from the sheet usingthe same laser. The heater has two separate resistive pathsfor two activation regions of the bidirectional actuator (eachhad a resistance 33 � and consumed 0.07 W to reach 75 ◦Cwithin 2 s). We designed each heater to share the ground

Figure 5. Inconel heater with an SMA actuator. Patterned Inconel heater with three electrodes, before (a) and after (b) mounting to anactuator. The bidirectional SMA actuator module on a robotic origami prototype (c).

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Smart Mater. Struct. 21 (2012) 065013 J K Paik and R J Wood

Figure 6. COMSOL simulation of (a) the heater model, 0.1 s heateractivation, (b) the epoxy bonded heater model (epoxy thickness0.08 mm), and (c) the epoxy bonded heater model (epoxy thickness0.12 mm).

line to minimize solder connections (see figure 5(a)). Theelectrode ends were 1 mm circles that were soldered ontoflex circuits mounted to the origami platform (figure 5(b)).This heater was mounted face down on the actuator’s foldingsides (see figure 5(c)). The heater path design, and wire andelectrode positions were customized for power consumptionand to match the geometry of the actuator substrate.

Bonding the flex-heaters to the SMA substrate was achallenge as NiTi is notorious for its poor solderability. Due

to the thin geometry and high strains, most pliable epoxiesor pressure sensitive adhesives failed after a single use. Weobserved improved bonding of the heaters using a microlaserwelder (Laser Star’s Nd:YAG laser welder with a minimumspot size 200 µm). To compliment the welds, we used atwo-part epoxy that was thermally conductive and electricallyinsulating (Cast-Coat Inc.’s CC3-300 with 40% maximumelongation). For the prototypes, we used a thin layer of epoxyto place the flex-heater first and welded the perimeter to theNiTi substrate.

4. Actuator modeling

We predict the behavior of the presented SMA actuatorby (a) heat flow modeling to explore the effect of oneheater on the adjacent section and (b) thermomechanicalmodeling of the response of the actuator to temperaturechanges. As we discussed in section 3, we used a combinationof laser-welding and adhesive to bond the heater to theactuator body and compared the heating speed for differentadhesive thicknesses. For the bidirectional SMA actuator,isolated heating regions are critical for producing independentmotions. This is a challenge that is exacerbated by therequirement that the rotational axes be in close proximity tomimic collinear rotations. We created COMSOL models withtwo sections of actuation which were actuated by two Inconelcircuits. We ran the model with three different adhesivethicknesses all operating at the same power input 0.075 W at0.22 A (0, 0.08, and 0.12 mm). We also observed the changeof the heater temperature with time.

Figure 6(a) shows the temperature distribution at 0.1 swhen the left heater was turned on. The activation region wasabove the alloy’s transition temperature, 65 ◦C. We observedminimal effect of the adhesive thickness variation on thetemperature distribution (see figures 6(b) and (c)). Thesetemperature distribution graphs are the simulations after 20 sof heating. The effect of epoxy thickness was only equivalentto 5% variation of the nominal power. We observed that thetemperature in the unheated region stayed below the transitiontemperature (even after 20 s) while the active regions requiredless than 2 s to activate. The middle slot in the actuatorserved as a mechanically critical feature during annealingand provided thermal isolation of the two actuating regions.In COMSOL, we observed that above 100 ◦C the heatertemperature started to affect the opposite region.

In order to model the thermomechanical effect of theSMA actuator, we assume that the strain is isolated alongthe axes of rotation and assume that the shape memory effectof each axis is independent of the other. Our analysis splitsthe SMA into thin layers and integrates the contribution ofeach layer to estimate the phase transition induced strain.Following the stress–strain and phase transformation modelof Leclercq et al [15], the strained area was assumed tobe passive and experiencing the thermomechanical couplingeffect through heat input q in (1) where q, Cv, λ, 1T , 1uare the applied thermal power, specific heat capacity, thermalconductivity coefficient, Laplacian temperature, and phase

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Smart Mater. Struct. 21 (2012) 065013 J K Paik and R J Wood

5mm

Figure 7. Bidirectional actuator modes: before activation (a) and (b), single axis activated (c) and both axes activated (d).

Figure 8. Angle response of four samples to a step input current;the shaded area indicates one standard deviation.

transformation latent heat respectively.

ρ(CvT −1uz) = q+ λ1T. (1)

In this energy balance equation [16], the thermal powerinput from the heater dictates the rate of change of the volumefraction of martensite phase, z, and the temperature change,and the last term of the equation depends on the externaltemperature.

Each layer of the actuator that is a distance y from theneutral axis has a strain as shown in (2), (3), where θ is thebending angle of the actuator, l is the length of the actuatingsection, and R is the radius of curvature where R0 is the radiusof curvature at the neutral axis

R0 =l

πand R =

l

π + θ(2)

εx(y) =

(y

R−

y

R0

)=

yθ

l. (3)

The stress generated in each layer due to bending is givenas (4) where E is the average Young’s modulus of all thephases and A is the cross-sectional area of the hinge that wasassumed to be constant during the transformation

σx(y) = E(εx(y)− γ zσ (y)). (4)

The changes of zσ (volume fraction of deformedmartensite) and zT (twinned martensite) are approximatedfunctions of the cosine of temperature change [17, 18]. Here,γ is the pseudo-plastic deformation coefficient and z is thevolume fraction of martensite. The torque generated (5) bythe actuator is equivalent to the total moment generated by

integrating the contribution of each infinitesimal layer

M = A∫ t

0σxy dy. (5)

5. Actuator experimental evaluation

The mechanical design and annealing process dictates theperformance of the SMA actuators. The bidirectional SMAactuator inherits most of the properties from a previouslydemonstrated single-axis torsional actuator [1], but with theadditional challenge of multiple thermal activation regionsin a single actuator. Therefore, it is critical to have bothregions thermally isolated from each other. The COMSOLmodeling described in section 4 predicts that the bidirectionalactuator should produce independent actuation at 65 ◦C (at0.06 W per region). However, even at 85 ◦C, we found that theactuator produced a faster response without interfering withits bidirectional functionality. Figure 7 displays two modes ofthe bidirectional actuator where selective heating enables theuser to actuate one or two opposing sides simultaneously.

In order to evaluate typical actuator metrics, we testedprototypes with the maximum heater temperature at 85 ◦Con one side of the actuator. On average, we found thefull range of motion of 0◦–180◦ was achieved within 2 s.Figure 8 displays the angular position of four prototypesunder a step current input. Repeated testing on a singleactuator showed little difference in the full actuation time.This number was a vast improvement from a NiCr coil heaterprototype that took about twice the time to produce the samerange of motion [1]: the thin and flat design of the Inconelheater produced concentrated heating to effectively thermallyactivate the actuator. Motion data were taken using a video andthe deflection angle was collected using ProAnalyst motionanalysis software.

Measuring the angular response to temperature change,we found the actuator displayed the shape memory effecteven before it reached the phase transition temperature.However, the maximum angular deflection was observedat the transition temperature of 65 ◦C. Figure 9 shows theactuator behavior at power input of 0.09 W. At this inputpower, the actuator reaches the transition temperature within1.8 s. When varying the power input, the transition trend wasthe same but the temperature ramp decreased or increasedwith the current supply.

However, the maximum angular deflection was observedat the transition temperature as shown in figure 9. When

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Smart Mater. Struct. 21 (2012) 065013 J K Paik and R J Wood

Figure 9. Temperature and angular displacement of the actuator.

Figure 10. Martensite-phase start and finish temperatures andaustenite-phase start and finish temperatures. Idealized curvesextrapolated from experimental phase transition observations.

Table 1. NiTi material properties.

Property Symbol Value

Specific heat capacity Cv 49 J kg−1

Thermal conductivity λ 10 W mK−1

Young’s modulus (average of allphases)

E 42 MPa

Pseudo-plastic deformationcoefficient

γ 0.05

Mass density ρ 6500 kg m−3

varying the power input, the transition trend was the samebut the temperature ramp was slower when less current wassupplied or faster when increased.

The thermomechanical model of the prototype requiredmaterial-specific phase transformation temperatures. Wefound these temperatures experimentally during heating andcooling post-annealed samples and observing their shapememory effect (figure 10).

We used the pseudo-plastic deformation coefficient givenby the manufacturer (see table 1) . These values determinedthe rate of change from martensite to austenite. The videoimages produced the measured strain values by measuringcurvature and using the relationship in (2) (figure 11). Themaximum strain of 20% was achieved at 180◦ deflection. Thecalculated and measured curves had comparable slopes.

We measured the blocked torque of the actuator andcompared it to the values found by (5). We used theexperimental setup used in [1] where the distal portion of

Figure 11. Measured and calculated strain values when suppliedwith 0.075 W at 0.22 A.

Figure 12. Experimental setup for measuring blocked torque. Theexerted force on the balance is recorded for corresponding angulardeflection [1].

Figure 13. Measured and calculated torques.

the actuator exerts a force on a precision scale (figure 12).The maximum torque was found when the actuator was lyingflat on the balance point where the reading was recorded forvarying power input. Figure 13 displays the exerted torque as afunction of power input. We observe that a higher power inputshowed a better match with the theoretical values. When thepower is small, the effect of power loss is more apparent and isobserved by a relatively large gap between the calculated andmeasured plot. Table 2 summarizes the actuator specifications.

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Smart Mater. Struct. 21 (2012) 065013 J K Paik and R J Wood

Table 2. Actuator specifications.

Property Value

Range of motion 0◦–180◦

Mass (with heater) 0.05 gActuation time constant ≈1 sPower consumption (no load) 0.092 W

6. Conclusion

This paper presents design considerations, fabricationprocesses, and experimental results of a bidirectionalSMA actuator. Having an external heater as a thermalactivation method, the actuator showed superior responsetime and power efficiency than conventional Joule-heatedSMA actuators—with relevance to small-scale roboticsapplications. The thin heaters created selective heating thatallowed the actuator to produce two distinct torques withina single actuator. The design of the actuator allowed for asimpler annealing process (compared even to a single-axisactuator [1]) while providing thermal isolation in twoactuating regions. The unique low profile of the prototype iscompatible with integration in a thin robotic origami structure.

Acknowledgments

This work was supported by the Defense Advanced ResearchProjects Agency (DARPA) under grant W911Nf-08-1-0228 (Programmable Matter) and the Wyss Institute forBiologically Inspired Engineering.

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